In a rectangular or Cartesian coordinate system (x,y,z), the *stress tensor* τ is given by:

where i_{x}, i_{y} and i_{z} denote unit vectors in the x-direction, y-direction and z-direction, respectively. The components of τ may be interpreted thus:

τ

_{xx}is the x-component of force per unit area exerted across a plane surface element normal to the x-direction;τ

_{xy}is the y-component of force per unit area exerted across a plane surface element normal to the x-direction; and so on. (Precisely analogous interpretations can be given to components of stress in any orthogonal coordinate system.)

Each component with identical suffices (τ_{xx}, τ_{yy} and τ_{ZZ}) is called a *normal stress* since it represents a force in a direction per unit area normal to that direction. Each other component with different suffices (τ_{xy}, τ_{yx}, τ_{xz}, τ_{zx}, τ_{yz} and τ_{zy}) is called a Shear Stress.

Heat & Mass Transfer, and Fluids Engineering